Use of representations in reasoning and problem solving: Analysis and improvement. (New Perspectives on Learning and Instruction Series) pages:74-93
This study examined students’ ability to make adaptive or flexible representational choices while solving linear-function problems. Two secondary-school classes solved problems under a choice (C-) condition, where they could choose a table, a graph, or a formula to solve each problem, and three no-choice (NC-) conditions (NC-table, NC-graph and NC-formula), where a predetermined representation had to be used. Data concerning representational efficiency (extracted from the NC-conditions) and frequency of representational choice (extracted from the C-condition) were analysed. Students’ representational flexibility was assessed using two conceptualisations of flexibility: A purely task-based conceptualisation, where choices were considered flexible if they took into account task characteristics alone, and a task student conceptualisation based on Siegler and Lemaire (1997), where student characteristics were also brought into the equation. The results obtained from both approaches are compared. Implications for research and education are discussed.